The strong approximation theorem and computing with linear groups

A. S. Detinko; D. L. Flannery; A. Hulpke

doi:10.1016/j.jalgebra.2019.04.011

The strong approximation theorem and computing with linear groups

A. S. Detinko, D. L. Flannery, A. Hulpke

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

2 Citations (Scopus)

Abstract

We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group H≤SL(n,Z) for n≥2. More generally, we are able to compute all congruence quotients of a finitely generated Zariski dense subgroup of SL(n,Q) for n>2.

Original language	English
Pages (from-to)	536-549
Number of pages	14
Journal	Journal of Algebra
Volume	529
DOIs	https://doi.org/10.1016/j.jalgebra.2019.04.011
Publication status	Published - 1 Jul 2019

Keywords

Algorithm
Linear group
Software
Strong approximation
Zariski density

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10.1016/j.jalgebra.2019.04.011

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title = "The strong approximation theorem and computing with linear groups",

abstract = "We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group H≤SL(n,Z) for n≥2. More generally, we are able to compute all congruence quotients of a finitely generated Zariski dense subgroup of SL(n,Q) for n>2.",

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AU - Flannery, D. L.

AU - Hulpke, A.

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N2 - We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group H≤SL(n,Z) for n≥2. More generally, we are able to compute all congruence quotients of a finitely generated Zariski dense subgroup of SL(n,Q) for n>2.

AB - We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group H≤SL(n,Z) for n≥2. More generally, we are able to compute all congruence quotients of a finitely generated Zariski dense subgroup of SL(n,Q) for n>2.

KW - Algorithm

KW - Linear group

KW - Software

KW - Strong approximation

KW - Zariski density

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VL - 529

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

The strong approximation theorem and computing with linear groups

Abstract

Keywords

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